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Domain and Range
The set of all possible input values (x) and the corresponding output values (y) of a function.
End Behavior
Describes what happens to y-values as x approaches positive or negative infinity.
Vertex Form of a Quadratic Function
y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Discriminant Formula
D = b² - 4ac, used to determine the nature of the roots of a quadratic equation.
Complex Numbers
Numbers that have a real part and an imaginary part, expressed as a + bi.
Quadratic Formula
x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.
Transformations of Functions
Changes to the graph of a function, including shifts, stretches, and reflections.
Inequality Notation
A way to describe the set of solutions that satisfy an inequality using symbols like ≤ or ≥.
Factoring Polynomials
The process of breaking down a polynomial into simpler components that, when multiplied together, give the original polynomial.
Systems of Equations
A set of equations with the same variables that are solved together.
Conic Sections
The curves obtained by intersecting a plane with a double-napped cone, including parabolas, circles, ellipses, and hyperbolas.
Quadratic Inequalities
Inequalities that involve quadratic expressions, often solved by finding intervals on a number line.
Absolute Value Function
A function that describes the distance of a number from zero, expressed as f(x) = |x|.
Polynomial Division
The process of dividing one polynomial by another, which can be done using long division or synthetic division.
Factoring by Grouping
A method of factoring polynomials with four terms by grouping pairs of terms together.
Asymptotes
Lines that a graph approaches but never touches, indicating behavior as it tends toward infinity.
Roots of a Quadratic Function
The values of x for which the quadratic function equals zero, found using the quadratic formula or factoring.
Vertex of a Parabola
The highest or lowest point on the graph of a quadratic function, represented by the coordinates (h, k).
Standard Form of a Quadratic Function
The form of a quadratic function written as y = ax² + bx + c.
Vertical Stretch and Compression
Changes in the steepness of the graph of a function, caused by multiplying the output of the function by a factor.
Horizontal Stretch and Compression
Changes in the width of the graph of a function, caused by multiplying the input of the function by a factor.
Zeroes of a Function
The x-values where the function's output is zero, also known as the x-intercepts.
Intercepts
Points where a graph crosses the x-axis (x-intercepts) or y-axis (y-intercept).
Quadratic Regression
A statistical method used to fit a quadratic equation to a set of data points.
Polynomial Functions
Functions that are represented by a polynomial equation, which can have one or more terms.
